To view the spin characters from a different perspective, it could be interesting to take \(\delta \in (M)\)  and consider \(\ker \delta \) . In the case for a surface \(S\) , the kernel of a character is in one-to-one correspondence with the set of maximal ideals of the algebra of holomorphic functions. Succinctly, we can match a character \(\delta _x\)  with the class of holomorphic functions \([f]\)  who vanish at the point \(x\) . The maximal ideals of the space of holomorphic functions are exactly the functions that vanish at just a single point. It is not clear that elements in \(\ker \delta \)  have this property when the dimension of \(M\)  exceeds 2. Part of the proof for the 2-dimensional result used by Belishev in [1]} follows from [2]} which can be proven using sheaves. To that end, it may be useful to think of the space \(^+(M)\)  in the context of sheaves.
